##
**
Common Values of Generalized Fibonacci and Leonardo Sequences
**

###
Bibhu Prasad Tripathy and Bijan Kumar Patel

Department of Mathematics

School of Applied Sciences

KIIT University Bhubaneswar

Odisha 751024

India

**Abstract:**

For an integer *k* ≥ 2, let
*F*_{n}^{(k)}
be the *k*-generalized Fibonacci
sequence that starts *n* with 0,..., 0, 1, 1 (*k* terms)
and each term
afterwards is the sum of *k* preceding terms. In this paper, we find all
the *k*-generalized Fibonacci numbers that are Leonardo numbers. More
explicitly, we solve the Diophantine equation
*F*_{n}^{(k)} = Le_{m}
in positive integers *n, k, m* with *k* ≥ 2.

**
Full version: pdf,
dvi,
ps,
latex
**

(Concerned with sequences
A000032
A000045
A001595.)

Received January 31 2023;
revised versions received February 8 2023; May 17 2023; May 26 2023.
Published in *Journal of Integer Sequences*,
June 12 2023.

Return to
**Journal of Integer Sequences home page**